# Expected number of shipments and its standard deviation

Recent history suggests that one supplier fails to meet this new specification 20% of the time. Assume that the next 15 batches of this alloy are a random sample.

How can I find the expected number of shipments that do meet the new specifications, and the standard deviation?

-
This question needs more information. What do you mean by "20% of the time"? is it 20% of the batches given by 1 supplier are bad, or that 20% of suppliers give batches which are all bad? And does 1 supplier give only 1 batch - or can they give multiple batches? And what is the random sample of? is it of 15 batches from 1 shipment, or a random selection of 15 batches from multiple shipments? –  probabilityislogic Apr 6 '11 at 13:28
A simple approach would be to assume that each shipment will meet the specification with $p = 1 - 20\% = 80\%$ probability. The number of shipments meeting the specification (k) will then follow a binomial distribution: k ~ B(15, 80%) and the expected value will be $n \cdot p = 15 \cdot 80\%=12$. The standard error of this estimate is the standard deviation of the binomial distribution: $\sqrt{n p (1 − p)} = 1.55$, however, k is not normally distributed.